Ternary representation improves the search for binary, one-dimensional density classifier cellular automata

Abstract

Standard practice for searching binary, one dimensional cellular automata rule space, relies on representing the candidate rule numbers by their corresponding binary sequence. Recently the use of ternary representation has been tried, which is based upon the traditional notion of schemata in genetic algorithms, though not with a focus on their effectiveness for the search. Here, we specifically go about such an evaluation, in the context of the classical benchmark task of density classification, in which the objective is to find a binary, one-dimensional rule that indicates the prevailing bit in a binary sequence, given to the rule as an initial configuration. The role of ternary representation is probed by comparing their introduction into two simple and traditional genetic algorithms of the literature, developed for the task. The experiments show that the ternary representation can lead to an increase in the number of high performance rules found for the task.